APR Calculator
The Rate That Includes What the Rate Sheet Doesn't
A loan's advertised nominal interest rate doesn't include origination fees, closing costs, or other charges deducted from what you actually receive. APR (Annual Percentage Rate) folds those fees into a single effective rate by finding the interest rate at which the present value of every scheduled payment equals what you actually walked away with — not the face amount of the loan.
The Formula
Net Received = Loan Amount − Fees
APR = the rate at which PV(all payments) = Net Received
Because this equation can't be solved algebraically for APR directly, the calculator uses a numerical search (bisection) to find the monthly rate that makes the present value of the fixed payment stream exactly equal the amount actually disbursed after fees.
Why APR Runs Higher Than the Nominal Rate
- Fees shrink what you receive, not what you owe — you still repay based on the full loan amount, but you only received the amount minus fees, which pushes the effective rate up.
- Shorter terms amplify the effect — the same dollar amount of fees has a bigger impact on APR for a 2-year loan than a 10-year loan, since there's less time to spread the cost.
- Comparing loans fairly — two loans with identical nominal rates but different fees will have different APRs; APR is the more accurate number for comparison shopping.
$10,000 Loan at 7% Nominal, 5-Year Term
| Fees | Net Received | APR |
|---|---|---|
| $0 | $10,000.00 | 7.0000% |
| $300 | $9,700.00 | 8.2861% |
With no fees, APR simply equals the nominal rate — the gap only appears once upfront costs reduce the amount actually received.
How to Use This Calculator
- Enter the Loan Amount.
- Enter the Nominal Annual Interest Rate.
- Enter the Loan Term in years.
- Optionally enter Fees / Closing Costs.
- Select Calculate to see the true APR.
Related Calculations
For the effective rate on a savings or investment account instead, see the Effective Interest Rate Calculator, or check a basic loan payment with the Loan Calculator.